A conducting sphere of radius `10 cm` is charged `10 muC`. Another uncharged sphere of radius `20 cm` is allowed to touch it for some tome. After that if the sphere are separted, then surface density of chsrges, on the spheres will be in the ratio of

Options

A. `1:4`
B. `1:3`
C. `2:1`
D. `1:1`

Answer

C

Explanation

Since, `Q prop ` radius
`implies Q._(1) =((10)/(10+20))xx10 =10/3muC`
` Q._(2) =((20)/(10+20))xx10 =20/3muC`
The ratio of charge density `[sigma = Q/(4pi r^2)]`
`sigma_1/sigma_2 = (Q_1.)/(Q._2)xxr_2^2/r_1^2 = (10//3)/(20//3)xx(20/10)^2 =2:1`